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Statistics

statistical-rethinking.md

Intro To Probability 1

What's the difference between probability and statistics? One way of describing it is putting as opposites, or complementary. In probability questions you have a "model", a way of describing how the world should be. In probability questions you don't have the "data", the set of results saying how the world is. In statistic questions you have the data, you have the set of results. In statistic questions you don't necessarily have the model, the way of describing the world.1

In statistic questions, you have your set of data, and from them you want to infer (work out), what the probability model is that would explain them.1

Frequentist

The frequentist view of probability, say for the chance of an event happening, is to study it over a period of time (look at a coin flip a hundred times), and then take the average.1

Bayesian / Subjectivist

This bayesian view of probability, is to say probability is the degree of belief that the event will happen.1

Probability Theory

Probability Distributions

  1. If we were to write a list (a set) of all possible events that could occur in a given situation, that would be called a "sample space".
  2. Any one of these individual events in this sample space would be called an "elementary event". One of the elementary events has to occur, but only one can occur.
  3. The chance of any individual elementary event occuring in this situation is the "probability". If the elementary event is \(X\), the probability of it is \(P(X)\)
  4. As one of the elementary events has to occur, it means the sum of all the probabilities in the sample space have to add up to one. This is the "law of total probability"
  5. If everything above has happened (we have a sample space, a list of elementary events, a probability for each event, and a total probability that adds up to one), then we have a "probability distribution".
  6. As well as an elementary event, there is also a non-elementary event. These are events that are a group of elementary events combined.1

Binomial Distribution

  • The binomial distribution is one type of probability distribution1

TODO: Section 9.4 onwards: https://learningstatisticswithr.com/book/probability.html#binomial

Sources

  1. Part Iv. Statistical Theory https://learningstatisticswithr.com/book/part-iv-statistical-theory.html ↩↩↩↩↩↩↩